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arXiv · 2405.04509

Asymptotic formula for the sum of a prime and a square-full number in short intervals

Fumi Ogihara·Yuta Suzuki
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Abstract

Let $R_{m, \mathrm{sq-full}}(N)$ be a representation function for the sum of a prime and a square-full number. In this article, we prove an asymptotic formula for the sum of $R_{m, \mathrm{sq-full}}(N)$ over positive integers $N$ in a short interval ($X$, $X+H$] of length $H$ slightly bigger than $X^{\frac{1}{2}}$.

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Fumi Ogihara, Yuta Suzuki. 2024-05-07. Asymptotic formula for the sum of a prime and a square-full number in short intervals. https://arxiv.org/abs/2405.04509

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